The Yates Abomination [culture]

Andrea Yates, the monster who drowned her entire brood of small children in her bathtub a few years ago, was given a new trial on appeal. Why? According to the AP:

Prosecutors have said they plan to once again call Dr. Park Dietz, the psychiatrist who testified at Yates' first trial that one episode of "Law & Order" depicting a woman who drowned her kids in a bathtub and was acquitted by reason of insanity aired before the Yates children died.

But no such episode existed, and the mistake caused an appeals court to overturn Yates' conviction.

This is amazing. Her conviction was overturned because a witness was mistaken about a television show?

Why does it much matter? There are two major issues in the case: first, did Yates kill her children (she did, and no one disputes it); second, was she ill at the time or not?

How could the existence or non-existence of aTV show episode be that important?